Index: The Book of Statistical ProofsProbability Distributions ▷ Univariate continuous distributions ▷ Normal distribution ▷ Probability density function

Theorem: Let $X$ be a random variable following a normal distribution:

$\label{eq:norm} X \sim \mathcal{N}(\mu, \sigma^2) \; .$

Then, the probability density function of $X$ is

$\label{eq:norm-pdf} f_X(x) = \frac{1}{\sqrt{2 \pi} \sigma} \cdot \exp \left[ -\frac{1}{2} \left( \frac{x-\mu}{\sigma} \right)^2 \right] \; .$

Proof: This follows directly from the definition of the normal distribution.

Sources:

Metadata: ID: P33 | shortcut: norm-pdf | author: JoramSoch | date: 2020-01-27, 15:15.